Circle P is tangent to the x-axis and the y-axis. If the coordinates of the center are (r, r), find the slope of the line through the origin and the center.

The area of the square is -128.

Final answer:

To solve the expression 12.5(18/6) + 5³, divide 18 by 6 to get 3. Multiply 12.5 by 3 to get 37.5. Then, calculate 5³, which equals 125. Adding the results, you get 162.5.

Explanation:

To solve the expression 12.5(18/6) + 5³, follow the order of operations (PEMDAS/BODMAS). First, divide 18 by 6, which equals 3. Next, multiply 12.5 by 3, which equals 37.5. Finally, calculate 5³, which equals 125. Adding the results, 37.5 + 125 = 162.5.

22cm is the greatest

It should be greater than17(20-3)

and smaller than 23(20+3)

Answer:

[tex](-9,-6)[/tex]

Step-by-step explanation:

We have been given an equation of a circle [tex](x+9)^2+(y+6)^2=225[/tex]. We are asked to find the coordinates of the center of the given circle.

We know that center-radius form of a circle is in format: [tex](x-h)^2+(y-k)^2=r^2[/tex], where,

[tex](h,k)=\text{Center of circle}[/tex],

[tex]r=\text{Radius of circle}[/tex]

Upon comparing our given equation with center-radius form of a circle we will get,

[tex](x-(-9))^2+(y-(-6))^2=15^2[/tex]

Therefore, the center of our given circle is at point [tex](-9,-6)[/tex].

Sample Response: Locate two corresponding ordered pairs of the two shapes. Calculate how much the pre-image values were multiplied by to obtain the image values. This is your scale factor. You can calculate this by dividing the coordinates of the mage by the corresponding coordinates of the pre-image.

The amount 16 ounce into grams using the conversion factor 1 ounce = 28.35 grams is 454.2 grams.

To convert ounces to grams, you can use the conversion factor:

1 ounce = 28.35 grams

Now, to convert 16 ounces to grams:

= 16 ounces * 28.35 grams/ounce

= 454.16 grams

Rounding to the nearest tenth:

454.16 grams rounded to the nearest tenth is 454.2 grams.

Therefore, the required quantity is 454.2 grams.

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To convert 16 ounces to grams, we multiply 16 by the conversion factor of 1 ounce to grams (28.35). This gives us 453.6 grams, when rounded to the nearest tenth.

To convert ounces to grams, we use the conversion factor 1 oz = 28.35 g. Given that we are converting 16 ounces to grams, we multiply the number of ounces by the conversion factor.

So, 16 oz * 28.35 g/oz = 453.6 g. Rounding to the nearest tenth, the result is 453.6 g.

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The volume of cylinder is 1962.5 [tex]cm^{2}[/tex].

To find the volume of a cylinder.

The part of geometry concerned with ascertaining lengths, areas, and volumes. Mensuration deals with the size, region, and density of different forms both 2D and 3D.

Given that:

Radius= 5 cm

Height= 0.25 m=25 cm

π=3.14

By the formula of volume of cylinder

Volume=π[tex]r^{2} h[/tex]

TO put the value,

Volume=3.14*5*5*25

Volume=1962.5 [tex]cm^{2}[/tex]

So, the volume of cylinder is 1962.5 [tex]cm^{2}[/tex].

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We have been given that

2 cups flour + 3 eggs + 1 tbs oil → 4 waffles

In order to make 4 waffles we need 3 eggs.

Thus, to make 1 waffle we need 3/4 eggs.

Now, in 1 dozen there are 12 waffles. Hence, to make 12 waffles we need

[tex]\frac{3}{4} \times 12\\ \\ =3 \times 3\\ =9[/tex]

Therefore, 9 eggs are needed to make 1 dozen waffles.

D is the correct option.

Final answer:

The correct option is (d) 9. Using the given recipe, we can determine that 9 eggs are needed to make 1 dozen waffles by setting up a proportion and solving for the number of eggs.

Explanation:

The original recipe provided states that 2 cups of flour, 3 eggs, and 1 tablespoon of oil will yield 4 waffles. To find out how many eggs are needed to make 1 dozen (12) waffles, we need to set up a proportion based on the given recipe.

Since 4 waffles require 3 eggs, we can set up the following equation: 4 waffles / 3 eggs = 12 waffles / x eggs. Cross-multiplying gives us 4x = 36, and dividing both sides by 4 gives us x = 9. Therefore, 9 eggs are required to make 1 dozen waffles.

The weight of the water in the cube-shaped aquarium will be 1674 lb, which is much greater than the table's maximum weight capacity of 200 lb. Therefore, the aquarium should not be placed on the table. The density of the water remains constant at 62 lb/ft³ regardless of how much the aquarium is filled.

To determine if the aquarium can be placed on a table with a weight limit of 200 lb, we must first calculate the weight of the water the aquarium will hold. We calculate the volume of the aquarium, then multiply it by the density of water, as the density is given as weight per unit volume (specifically 62 lb/ft³).

The volume (V) of a cube is given by V = side³, so for our aquarium with 3 ft long edges, V = 3³ = 27 ft³. The weight of the water (W) is therefore W = density x volume = 62 lb/ft³ x 27 ft³ = 1674 lb. Since 1674 lb exceeds the table's maximum weight capacity of 200 lb, the aquarium should not be placed on the table.

As for part (b), the density of the water does not change whether the aquarium is full or half full. Density is an intensive property meaning it's independent of the quantity of the substance present. Therefore, whether the aquarium is filled or only half filled, the density of the water remains at 62 lb/ft³.

Answer:

x = 3/2

Step-by-step explanation:

That is quite long and drawn out, so we have to get it down to a single quadratic equation, set equal to 0.

Begin by expanding the right side to get

[tex]y+3x-6=-3(x^2-4x+4)+4[/tex]

then multiplying in the -3 to get

[tex]y+3x-6=-3x^2+12x-12+4[/tex]

Now we will combine all the like terms and get everything on one side of the equals sign, and set it equal to 0:

[tex]-3x^2+9x-2=0[/tex]

In order to find the equation of the axis of symmetry we have to put it into vertex form, which is accomplished by completing the square on this quadratic.

In order to complete the square, the leading coefficient has to be a +1.  Ours is a -3, so we will factor that out.  First, though, now that it is set to equal 0, we will move the constant, -2, over to the other side, isolating the x terms.

[tex]-3x^2+9x=2[/tex]

Now we can factor out the -3:

[tex]-3(x^2-3x)=2[/tex]

The rules for completing the square are as follows:

Take half the linear term, square it, and add it to both sides.  Our linear term is 3.  Half of 3 is 3/2, and squaring that gives you 9/4.  We add into the parenthesis on the left a 9/4, but don't forget about that -3 hanging around out front that refuses to be ignored.  We didn't add in just a 9/4, we added in (-3)(9/4) = -27/4:

[tex]-3(x^2-3x+\frac{9}{4})=2-\frac{27}{4}[/tex]

In the process of completing the square we created a perfect square binomial on the left.  Stating that binomial and simplifying the addition on the right gives us:

[tex]-3(x-\frac{3}{2})^2=-\frac{19}{4}[/tex]

We can determine the axis of symmetry at this point.  Because this is a positive x-squared polynomial, the axis of symmetry is in the form of (x = ) and what it equals is the h coordinate of the vertex.  Our h coordinate is 3/2; therefore, the axis of symmetry has the equation x = 3/2

Answer:

The correct option is a.

Step-by-step explanation:

The general form of a quadratic regression equation is

[tex]y=ax^2+bx+c[/tex]                         ..... (1)

Using graphing calculator we get

[tex]a=-0.143393\approx -0.143[/tex]

[tex]b=0.59525\approx 0.595[/tex]

[tex]c=2.82964\approx 2.830[/tex]

Substitute these values in equation (1) to find the quadratic regression equation for this data set.

[tex]y=-0.143x^2+0.595x+2.830[/tex]

Therefore the correct option is a.